Find roots of polynomial $$ p(x) = x^7-x^6+x^5+x^4+x^3+x^2+2x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.0517\\[1 em]x_2 &= 0.4671+1.2293i\\[1 em]x_3 &= 0.4671-1.2293i\\[1 em]x_4 &= -0.6429+0.8975i\\[1 em]x_5 &= -0.6429-0.8975i\\[1 em]x_6 &= 1.2016+0.9008i\\[1 em]x_7 &= 1.2016-0.9008i \end{aligned} $$Explanation
Polynomial $ x^7-x^6+x^5+x^4+x^3+x^2+2x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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